I don't understand this question. Are you making up the notes? Or are singing the song as composed? Do you still have this question if there is a lyric sheet with all the "in between notes" for the chords and you follow those notes (i.e. is it important to the question that there is just a chord sheet with no notes)? If you're making up those notes, you're the improviser/composer: you tell me what the relationship is.
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KazJul 26 '14 at 15:30

This topic is too broad; maybe you want to narrow it down to a question about several chords, and a particular melody that you sang which you think "works", the question being why those notes work with those chords.
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KazJul 26 '14 at 15:44

I'm singing the song as composed. Yes I have the same question if the sheet music is right in front of me. I want to know the relationship between the sheet music and the chords. I asked about singing because that's my specific practical application. However the basic premise is the relationship between sheet music and chords.
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StaceyJul 26 '14 at 15:49

@Kaz Another way of putting it: if I were to compose the in-between notes, what notes would work musically. I just want to know why certain chords work with certain notes.
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StaceyJul 26 '14 at 15:52

This subject fills books, and is a big chunk of what music theory is about, at least Western; so it's not a good Q&A format. You can find good notes simply by trial and error: generate some ideas, and give them a critical listen. If you do that for years, you build a vocabulary of phrases. The theory comes later: it tries to classify and explain why people like how certain things sound and how they might actually be related to other, seemingly different ones. Then, in turn, it is possible to use the theory as a guide in creativity.
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KazJul 27 '14 at 0:26

2 Answers
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Vocal melodies (or any melodies, for that matter) are likely to use the notes within accompanying chords to some extent. However, melodies are unlikely to only use notes within the accompanying harmony (chords). In fact, melodies would be rather dull if they did! Depending upon the style or genre of music, and also the adventurousness of the composer (I guess), melodies may contain a greater or lesser amount of non-chord tones, notes that aren't in the accompanying chord. Non-chord tones are most likely to be other notes from the key the music is in at that point, or they may even be chromatic within that key.

To illustrate these ideas, here are some examples. Let's say the chord accompanying your melody is an E Major chord, at some point in a piece of music. This chord contains the notes E (root), G# (maj3) and B (5). These are the chord tones; the melody part could just use these notes, although this is unlikely to be very interesting, as it would essentially be restricted to arpeggiating the notes of an E Major chord or even fewer notes. If your E Major chord is part of a chord progression in the key of E Major it could easily use non-chord tones that are also from the key of E Major; these other E Major notes would be F#, A, C# and D#. Non-chord tones can relate to chord tones in a number of ways, for instance as: passing notes; suspensions/retardations; auxiliary notes. (It is worth pointing out that non-chord tones need not be related to a chord-tone in one of these ways; instead they may simply be an extension of the harmony, essentially creating an extended or added chord when combined with the accompanying chord.) Finally, the melody could contain notes neither within the accompanying chord or the current key of the music; these would be chromatic to the key. In this case they would be the notes not in E Major: F, G, Bb, C and D (or their enharmonic equivalents). These would be less likely to be used, but could still certainly be in the melody part. If they are used, it is likely that they would need to resolve effectively to either chord-tones or certainly other notes within the underlying key of the music. Of course, it could also be that the E Major chord is within another key (for instance: A Major, A Minor or B Major, to name just a few). Obviously this would change the non-chord tones likely to be used (i.e. the non-chromatic ones).

Finally, it is worth noting that the chord used at any point within a piece or song, may itself be chromatic to a certain overall key. (Where other chords more strongly define a particular key.) And a major scale (or even other diatonic modes) certainly need not be the only way to organise melody notes or chords in a piece of music. Popular music styles make use of a wide variety of different scales/modes in addition to "traditional" major and minor keys.

To Bob's fine answer I would only add that non-chord tones typically 'resolve' into chord-tones, or are supported by being added into the chord voicing as well.
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GreyJul 26 '14 at 11:48

How does a chord resolve into another? I am familiar with suspended chords resolving, they feel/sound unfinished until resolved. Is this what you are referring to? Can non-sus chords resolve?
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StaceyJul 26 '14 at 11:56

@Grey Actually, thinking about it some more, you're referring to individual notes resolving rather than chords. I think I understand what you mean, some notes I sing do have a feel of unfinishedness. As if it is necessary to sing another note to not leave it hanging. is this right?
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StaceyJul 26 '14 at 12:00

Yes. If you play a chord and sing a note NOT in the chord you will most likely feel that the note you are singing is not supported, and wants to 'resolve' to one of the notes in the chord. This is a different kind of resolution.
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GreyJul 26 '14 at 13:54

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One of my favourite singers for doing this is Bjork, she seems to find a lot of notes in her melodies that aren't in the underlying chords!
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Bob BroadleyJul 26 '14 at 16:02

While you do sing many notes a chord is composed of at least 3 notes and forms the harmony to support the melody(the notes you sing). The chord being played will not only support the melody, but it will help give the song a tonal center. Any melody can have harmonic tones(chord tones) or non-harmonic tones(non-chord tones).

A harmonic tone is a note in the chord (harmony). A non-harmonic tone is a note not in the chord (harmony).

It will always vary depending on what you are singing, but typically over half of the notes you sing will be in the underlying chord (harmony).